Cyclic Polygonal Designs with Block Size 3 and Joint Distance α = 2

Abstract

Polygonal designs are useful in survey sampling in terms of balanced sampling plans excluding contiguous units (BSECs) and balanced sampling plans excluding adjacent units (BSAs). In this article, the method of cyclic shifts has been used for the construction of cyclic polygonal designs (in terms of BSAs) with block size k = 3 and λ = 1, 2, 3, 4, 6, 12 for joint distance α = 2 and 51 new designs for treatments v ≤ 100 are given.

Keywords:

• Cyclic BSA
• Cyclic polygonal designs
• Cyclic shifts
• Distance between the units
• Joint distance
• PBIBD

Mathematics Subject Classification:

• 05B05
• 62K05
• 62K10

Acknowledgments

The authors are grateful to the reviewers for their suggestions and for giving very useful comments which have helped in the improvement of the article.

Notes

where f stands for fractional (or smaller) CPDs.